Related papers: Infinite Geraghty type extensions and its applicat…
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
It is shown that the expansion methods developed in refs. arXiv:hep-th/0212347 and arXiv:hep-th/0401033v2 can be generalized so that they permit to study the expansion of algebras of loops, both when the compact finite-dimensional algebra…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.
The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.
This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…
We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.
In this work we derive and evaluate some infinite integrals involving the product of a generalized logarithm and polynomial functions in the denominator. These integrals are expressed in terms of finite series involving the Hurwitz-Lerch…
The first part of this thesis proposes a general approach to infinite dimensional non-Gaussian analysis, including the Poissonian case. In particular distribution theory is developed. Using appropriate integral transformations, generalized…
We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by…
We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.
In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications.
Infinitesimal bendings for classes of two-dimensional surfaces in $\mathbb{R}^3$ are investigated. The techniques used to construct the bending fields include reduction to solvability of Bers-Vekua type equations and systems of differential…
In this paper we construct a class of infinite-dimensional Frobenius manifolds in the spaces of pairs of meromorphic functions defined on certain regions of the Riemann sphere. For such Frobenius manifolds, we obtain their principal…
Formulations of some Grassmann-valued systems of ordinary differential equations invariant under (infinitesimal) supersymmetry transformations, including $N$-superspace extended types, are reviewed and discussed, with use of superfields.…
The method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential --- an analytic function in an infinite multiply connected domain with a simple pole at infinity which maps…
In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…
We give infinite dimensional and finite dimensional examples of $F-$fold Lie superalgebras. The finite dimensional examples are obtained by an inductive procedure from Lie algebras and Lie superalgebras.
The universal method of expansion of integrals is suggested. It allows in particular to derive the threshold expansion of Feynman integrals.
We investigate the Schr\"odinger representations of certain infinite-dimensional Heisenberg groups, using their corresponding Wigner transforms.